By a direct computation, which is in analogy with Lemma 1 of [1]}, we have
\( \Vert D_y\Psi (0,0)(Y^{\prime })\Vert =|-A^{-1}Y^{\prime }(\theta +\alpha )A+Y^{\prime }(\theta )|_{r}\ge \tilde{\eta }|Y^{\prime }|_{r}, \) 
